at one end there will be arduino with BT module and Mic with amplifier
So, you are expecting the Arduino to sample the audio data and send the digitized sample through the BT device at a rate fast enough to result in recognizable sounds at the other end. Good luck with that.
A few minutes with paper and pencil, and knowledge of the speed that you can transmit data via BT (115200 bytes per second), will tell you how many samples you need to take per second. Comparing this with the rate that the Arduino's analog to digital converter can sample the analog (audio) stream will tell you whether your project is feasible (or not).
I'm guessing that the "or not" is the result of your paperwork.